Friday morning I ran our 2001 Impala to warm up the engine to defrost the windows and the cabin lights (one above each of the back doors, and two on the bottom of the center rear view mirror) all would not come on when I opened the door or when I tried to turn them on with the headlight/cabinlight switch. I ran the engine for a while, while I cleared off the snow and ice from all the windows. When I opened the door to get back in the cabin lights came on (except for the one above the back passengers door which must be burned out). After I closed the door and the cabin lights went out I tried the headlight/cabinlight switch and the cabin light would come on when I selected them.

What could be going bad that caused the cabin lights to temporally not work?

I had a very similar problem with our 1992 Olds 88. Problem turned out to be a common splice point shared by the rear defroster and the interior lights. Apparently, the wiring was undersized from the factory and after X number of uses, the wiring deteriorated and since it began pulling too much current, it overheated the circuit, tripping a thermal circuit breaker. After the rear defroster timed off, the circuit & circuit breaker cooled down and the interior lights returned to normal operation.